Structurally Nonlinear Fluttering Airfoil in Turbulent Flow

Abstract

The dynamics and response of a structurally nonlinear two-dimensional airfoil in turbulent flow are investigated numerically. The solution is analyzed in terms of probability density function (PDF), response mean square, power spectral density, and Lyapunov exponent. Both the longitudinal and vertical components of turbulence are considered. It is shown that turbulent flow, due to its longitudinal component, diminishes the stability of the aeroelastic system by advancing the flutter point and decreasing the damping, thus confirming results from previous work where only the longitudinal component was modeled. Furthermore, the shift in flutter airspeed is strongly dependent on the random stiffness terms. It is also observed that turbulence may advance the airspeed at which the pitch angle marginal PDF changes from uni- to bimodal compared with the nonexcited deterministic case, whereas the heave transition appears to be postponed. This observation is attributed to the nonlinearity considered, a cubic stiffness in torsion. Finally, in terms of response mean square, the system appears to he more sensitive to the presence of the longitudinal excitation component at pre- rather than at postinstability airspeeds.